A new version for F|ReS & ector's Dolphin homebrew for the Wii is now out for your consumption. This version, r748, removes the disable-alpha bools in virtual copy shaders.

Dolphin is actually workable on both the Wii and the NGC. It also features partial Wii support, and plays most Gamecube games smoothly.

Further features include:

• Supports DOL/ELF, Gamecube + Wii disc images / physical backup discs, Wii system menu / channels, and WADs.
• Debuggers for PowerPC, DSP, and graphics processors
  • Interpreters and recompilers for each processor
  • OpenGL, DirectX, and software renderers with graphical enhancements and debugging features.
• Action Replay Simulator / Gecko Code Interpreter
• Gamecube Memory Card Manager
• Real and emulated Wiimote support
• Gamepad support (including Xbox 360 pad)
• Experimental NetPlay
• Save states

As for the system requirements:

• Windows XP or higher, or Linux, or OS X (Intel only).
• Fast modern CPU with SSE2. Multiple cores for a speed boost.
• Any reasonable modern GPU with Pixel Shader 2.0 or greater. nVidia or ATI are good. Older integrated Intel chips may not work, newer ones should work fine.